A rectangular prism has a base area of 15 cm² and pyramid with a congruent base and height has a volume of 20 cm³ What is the height of the rectangular prism?
A. 4/3 cm
B. 20 cm
C. 4 cm
D. 5 cm
C. 4 cm
Firstly, we need to determine the dimensions of the base of the pyramid. Since the base area of the prism and the pyramid are congruent, the base area of the pyramid is also 15 cm².
Let the base of the pyramid be a square with side length s. Therefore, s² = 15. So, s = √15.
Now, we know that the volume of a pyramid is (1/3) * base area * height. Plugging in the values we have:
20 = (1/3) * 15 * h
60 = 15h
h = 4 cm
Therefore, the height of the rectangular prism is 4 cm.